A block of mass rests against a horizontal ideal spring with force constant
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A block of mass 0.50kg rests against a horizontal ideal spring with force constant k=200Nm−1. The spring is compressed 0.10m from its natural length and then released. The block slides across a horizontal tabletop with two distinct regions:
• Region I: a 0.25m-long rough patch with coefficient of kinetic friction μk=0.20 begins exactly where the spring returns to its natural length.
• Region II: a frictionless surface extends beyond Region I.
Assume the spring is fixed to a wall and does not move after returning to its natural length.
(a) Determine the speed of the block at the instant it leaves the spring (spring at natural length).
(b) Calculate the speed of the block immediately after it exits Region I.
(c) Describe qualitatively how the block’s speed would change if the rough patch were twice as long but had the same coefficient of friction. No calculation is required, but base your explanation on energy considerations.